Constraints Between Equations of State and Mass-Radius Relationships in General Clusters of Stellar Systems

TL;DR

This paper establishes fundamental constraints on the equations of state for stellar clusters that follow specific mass-radius relationships, with broad applicability and practical implications for observed stellar systems.

Contribution

It provides general obstruction theorems linking equations of state to mass-radius bounds in stellar clusters, extending previous results and applying to real data.

Findings

Proved three general obstruction theorems for equations of state

Applied results to real stellar system data

Identified limitations on possible mass-radius configurations

Abstract

In this article we prove three obstruction results on the existence of equations of state in clusters of stellar systems fulfilling mass-radius relationships and some additional bound (on the mass, on the radius or a causal bound). The theorems are proved in large generality. We start with a motivating example of TOV systems and we close by applying our results in stellar systems arising from experimental data.